Semi-competing risks refer to the phenomenon where a primary outcome event (such as mortality) can truncate an intermediate event (such as relapse of a disease), but not vice versa. Under the multi-state model, the primary event is decomposed to a direct outcome event and an indirect outcome event through intermediate events. Within this framework, we show that the total treatment effect on the cumulative incidence of the primary event can be decomposed into three separable pathway effects, corresponding to treatment effects on population-level transition rates between states. We next propose estimators for the counterfactual cumulative incidences of the primary event under hypothetical treatments by generalized Nelson-Aalen estimators with inverse probability weighting, and then derive the consistency and asymptotic normality of these estimators. Finally, we propose hypothesis testing procedures on these separable pathway effects based on logrank statistics. We have conducted extensive simulation studies to demonstrate the validity and superior performance of our new method compared with existing methods. As an illustration of its potential usefulness, the proposed method is applied to compare effects of different allogeneic stem cell transplantation types on overall survival after transplantation.
We investigate how exposure to the One-Child Policy (OCP) during early adulthood affects marriage and fertility in China. Exploring fertility penalties across provinces over time and the different implementations by ethnicity, we show that the OCP significantly increases the unmarried rate among the Han ethnicity but not among the minorities. The OCP increases Han-minority marriages in regions where Han-minority couples are allowed for an additional child, but the impact is smaller in other regions. Finally, the deadweight loss caused by lower fertility accounts for 10 percent of annual household incomes, and policy-induced fewer marriages contribute to 30 percent of the fertility decline.
Order type plays an important role in algorithmic trading and is a key factor of price impact. In this paper, we propose a new framework for studying the discrete price change process, which focuses on the impacts of aggressive orders (market orders and aggressive limit orders) and cancellations. The price change process is driven by states and events of best quotes, and we define the event-based price change as the "natural price change" (NPC). Under the framework, we propose a heteroscedastic linear econometric model for the NPC to explore the impact of different types of orders on the price dynamics. To verify the usability of our model and explore the driving factors of price dynamics, we conduct a thorough empirical analysis for 786 large-tick stocks traded on the Shenzhen Stock Exchange. Empirical results statistically demonstrate that aggressive orders can introduce stronger impact on the NPC than cancellations. Meanwhile, splitting a big order into several small orders can lead to a larger NPC. Our framework can also be applied for the prediction of price change.